Nathan Garnett, via e-mail:
I showed students a few pictures of the Luxor Hotel in Las Vegas, and then I asked them how long they it would take to wash all of those windows. We did lots of math. I had a student clean a 2ft by 5ft section of the board (with windex sound effects) so we could get a cleaning time per 10 square feet. It was a blast.
Great work. We can do something similar with Pyramid of Pennies. Students are often curious how long it took to make the pyramid. So we give students enough pennies to make the top two layers. We time them. Then they use proportions to answer how long it would take them to make the entire pyramid.
And then we list all the reasons that answer is wrong.
It doesn’t account for bathroom breaks. For sleeping. For eating. For the fact that the top two layers are small and easy but the bottom ones require scaffolding and much, much more care.
Those exceptions aren’t reasons to not ask the question. Those exceptions make the question more messy, more meaningful, more like actual modeling, and less like textbook modeling where air resistance is neglected, the rates are constant, the men are strong, and the women lithesome.
We need more messy modeling tasks like Nathan Garnett’s.